Distributed Container Failure Models for the Dust-ms Computer Code

Improvements to the DUST-MS computer code have been made that permit simulation of distributed container failure rates. The new models permit instant failure of all containers within a computational volume, uniform failure of these containers over time, or a normal distribution in container failures. Incorporation of a distributed failure model requires wasteform releases to be calculated using a convolution integral. In addition, the models permit a unique time of emplacement for each modeled container and allow a fraction of the containers to fail at emplacement. Implementation of these models, verification testing, and an example problem comparing releases from a wasteform with a two-species decay chain as a function of failure distribution are presented in the paper. INTRODUCTION Disposal of low-level radioactive (LLW) wastes requires a demonstration that environmental concentrations of radionuclides do not exceed regulatory limits chosen to ensure the protection of public health. This requires the quantitative assessment of the potential radiological impact of a LLW disposal facility on the surrounding environment. Evaluation of these impacts is accomplished through a performance assessment which includes estimates of the following processes for each radionuclide: (a) the rate of release from the disposal unit (i.e., the source term); (b) the transport from the disposal unit to the accessible environment; and (c) the conversion of the radionuclide concentration at the receptor site into an equivalent dose. The objective of the DUST-MS (Disposal Unit Source Term – Multiple Species) computer model is to provide a tool that estimates the radionuclide release rate from the disposal facility, that is, the source term (1). In general, the source term is influenced by the radionuclide inventory and its origin (i.e., waste stream), the wasteforms and containers used to dispose of the inventory, and the physical processes that lead to release from the facility. DUST-MS may also be used to simulate transport through the unsaturated zone down to the aquifer. In addition, a recent improvement to DUST-MS includes a feature that creates an output file of mass flux at specified locations (1). Through selecting the proper location, (i.e. at the top of the aquifer), DUST-MS can be run a second time to simulate transport in the aquifer and the output file containing mass flux va lues from the first simulation (disposal facility and unsaturated zone) can be used as the inlet boundary condition for the second simulation (aquifer zone). This approach conserves mass between the two simulations. The models selected to represent the four major processes (fluid flow, container degradation, wasteform leaching, and radionuclide transport) influencing release and transport have been incorporated into the computer code DUST-MS. Wasteform release is modeled through three release mechanisms: a) a surface rinse process in which radionuclides are released upon contact with the solution, partitioning between the wasteform and solution can be modeled; b) diffusion controlled release from the wasteform; and c) uniform release in which a fixed fraction of the inventory is released every year. * This work was performed under the auspices of the U.S. Department of Energy. All of these release mechanisms account for radioactive decay and ingrowth of the source. In addition, a check is performed to insure that releases do not cause concentrations to exceed a user-defined solubility limit. Transport is modeled using a one-dimensional finite-difference solution of the advection/dispersion equation. The model considers the physical/chemical processes of advection, diffusion, dispersion, radioactive decay and ingrowth, and external sources (wasteform release rates) and sinks. Through support provided by Idaho National Engineering and Environmental Laboratory (INEEL), improvements have been made to the container failure model in DUST-MS. These include: a) Allowing a unique burial time for each container. In practice, a disposal site may be open for many years. Inventory values are reported at the time of disposal. The improved model permits a user to specify a problem start time (i.e., time at which waste was first disposed) and a disposal time for each container. This improves the accuracy for calculating releases radionuclides that have a half-life on the order of the operational time of the facility or less. b) Allowing time-distributed container failures. In previous versions of the model, container degradation was modeled through a unique container failure time. The value for this parameter should be selected based on the materials and expected environment. It was recognized that in using the one-dimensional DUST-MS code a single modeled container often represents a series of containers. In practice the failure time of each container in the series will be different. To accommodate this, DUST-MS was generalized to permit a distribution of container failures. The distribution will be specified using either a uniform failure rate or a Gaussian (normal) distribution characterized by a mean and standard deviation. c) Allowing a fraction of the containers to fail on emplacement. Experience has indicated that often a small fraction of the containers fail either due to emplacement practices or soon after emplacement. The improved models in DUST-MS permit the user to specify an initial failure fraction while allowing the remainder to fail based on the selected distribution and input parameters. This paper presents the improved container failure models and discusses their implementation in DUSTMS. The distribution in container failure times requires that wasteform release calculations be calculated using a convolution integral. The approach used in DUST-MS to accomplish this is also presented. Extensive verification tests were performed covering all four leaching models in DUST-MS (rinse, diffusion, uniform, and solubility limited) and the effects of ingrowth in the wasteform prior to release. Results of the verification tests are presented. This is followed by a discussion of the importance of distributed failure on release and performance assessment. Finally, an example of the effects of failure rate is presented for a two-species decay chain in which the first species has a half-life less than the mean container failure time. CONTAINER FAILURE MODELS DUST-MS is a one-dimensional (1-D) model that predicts the release and transport of contaminants disposed in the subsurface. The conceptual model collapses the 3-D physical system down to 1-D mathematical representation. This implies that there are frequently multiple containers represented in one computational cell by a single effective container. This effective container can fail at a specified time that represents the mean time to failure of all containers represented in the computational volume. However, in practice it is probable that the containers will fail over a distribution of times. To account for this, the single failure time is generalized to a distribution of failure times. In theory, the distribution can be any function. In most cases, the distribution of failure time approximates known statistical distribution functions such as the uniform, normal, lognormal, or exponential distribution functions. In DUST-MS three failure distributions are permitted: instantaneous, uniform, or normal. a) Instantaneous failure of all containers at time tj The failure distribution function, which represents the rate of change in container failures as a function of time, is: ) ( ) ( j j t t t t f − = − δ (1) where δ(t-tj) is the Kronicker delta function. The only information required for this model is the time to failure. This is the release rate for a single failure time for all containers and is the model in the previous versions of DUST-MS. b) Uniform Container Failure Rate The containers fail at a uniform rate from the beginning time of failure, tb , to the ending time of failures, te. The failure distribution function is: